A diatomaceous earth filter looks like your best bet then. It'll remove particles you didn't even know were there and reduce turbidity without affecting the tannins you want. I used on extensively when I participated in competitions and was always amazed at how much clearer the water got when I thought it was already clear.
Thanks for the tip but this sounds too complicated and I don't have much space left inside my cabinet and I don't want to add more stuff into aquarium. Hopefully my second external filter will handle this. Fingers crossed.